1.) Sega represented themselves on all of the competing systems beyond the Dreamcast at the time when they went multi-platform. Each system has their own plethora of DC ports, Naomi ports, and Exclusives. The PS2 is actually the most highly decorated Sega system after they went software only. This is why we have a Sega Games on PS2 forum

2.) I don't think there was much "liking" involved. It was a business decision for them to release games on the GameCube.

Below is a complete list of how Sega represented themselves on the GameCube:

Multi-Platform Sega Games [GC + Other Systems]

Phantasy Star Online Episode I & II (Sonic Team)

Phantasy Star Online Episode I & II Plus (Sonic Team)

Shadow the Hedgehog (Sonic Team USA)

Sonic Gems Collection

Sonic Heroes (Sonic Team)

Sonic Mega Collection

Sonic Riders (Sonic Team USA)

Super Monkey Ball (Amusement Vision)

Super Monkey Ball 2 (Amusement Vision)

GameCube Exclusives

Amazing Island (Hitmaker)

Beach Spikers (Sega AM2)

Billy Hatcher and the Giant Egg (Sonic Team)

F-Zero GX (Amusement Vision)

Phantasy Star Online Episode III: C.A.R.D. Revolution (Sonic Team)

Virtua Striker 2002 (Hitmaker)

Dreamcast Ports by Sega

Puyo Pop Fever (Sonic Team - unconfirmed, could have been Milestone or other)

Skies of Arcadia Legends (Sega WoW)

Sonic Adventure 2 Battle (Sonic Team)

Sonic Adventure DX Director's Cut (Sonic Team)

Dreamcast Ports by Activision

Crazy Taxi (Hitmaker) - runs a bit smoother than the DC version, overall decent port from what I can tell, may require further research

Super Monkey Ball Adventure (Traveller's Tales) - I personally don't even own this game. It goes against what the DC represented. It is western developed and the textures are so muddy looking that it detracts from the vibrant colors of the original Super Monkey Ball.

3rd Party - Here I think a firm line has to be drawn. Titles like Chaos Field, CVS2, and Shikigami no Shiro 2 were released on all platforms of the day. Also, the 2K sports series were ported to other systems to start an EA-esque serialization of the 2K games. I feel their originality ceased once they broke out into open waters so to speak. I think the only 3rd party games that can really qualify here are the NAOMI ports and Evolution Worlds. If we get into Guantlet and Kao the Kangaroo sequels we are starting to grasp for straws.

I wasn't trying to imply that Sega preferred the Gamecube over other systems, it was just my personal feeling that the Gamecube reminds me a lot of the Dreamcast and the fact that many Sega games (and the types of games) were released for it, reinforces that feeling.

Sega had a strong presence on each of the consoles of the Dreamcast's generation. I own a gamecube because it has many great games, but I also own a GameCube because I am very much a Sega fan, and Sega has many games on the GameCube that are worth owning.